Horizontal circular motionEdexcel International A Level Further Maths: Mind map

Exam questions on Horizontal circular motion

1. A particle of mass $0.5$ kg is attached to one end of a light inextensible string of length $2$ m. The other end of the string is fixed to a point $O$ on a smooth horizontal table. The particle moves on the table in a circle with centre $O$, at a constant speed of $4$ m s$^{-1}$.
   The speed of the particle is increased until the tension in the string is three times its original value. Find the new speed.2 marks
2. A particle of mass $0.4$ kg is attached to one end of a light inextensible string of length $2.45$ m. The other end of the string is fixed. The particle moves in a horizontal circle with constant angular speed, with the string inclined at an angle $\theta$ to the vertical, where $\cos\theta=0.8$. Take $g=9.8$ m s$^{-2}$.
   Find the angular speed of the particle.2 marks
3. A car of mass $800$ kg is modelled as a particle moving in a horizontal circle of radius $60$ m on a road banked at an angle $\alpha$ to the horizontal, where $\tan\alpha=\frac14$. Take $g=9.8$ m s$^{-2}$.
   Find the speed at which the car can travel round the bend with no tendency to slip sideways.3 marks